Funnel control of nonlinear systems

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by $r$-th order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems)

Funnel control of nonlinear systems

Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by r-th-order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone input effects. A control structure is developed which ensures that, for every member of the underlying system class and every admissible reference signal, the tracking error evolves in a prescribed funnel chosen to reflect transient and asymptotic accuracy objectives. Two fundamental properties underpin the system class: bounded-input bounded-output stable internal dynamics, and a high-gain property (an antecedent of which is the concept of sign-definite high-frequency gain in the context of linear systems)

PID control of second-order systems with hysteresis

The efficacy of proportional, integral and derivative (PID) control for set point regulation and disturbance rejection is investigated in a context of second-order systems with hysteretic components. Two basic structures are studied: in the first, the hysteretic component resides (internally) in the restoring force action of the system ('hysteretic spring' effects); in the second, the hysteretic component resides (externally) in the input channel (e.g. piezo-electric actuators). In each case, robust conditions on the PID gains, explicitly formulated in terms of the system data, are determined under which asymptotic tracking of constant reference signals and rejection of constant disturbance signals is guaranteed. Keywords: hysteresis; non-linear systems; PID control; tuning regulator

Synthetic lethal analysis of Caenorhabditis elegans posterior embryonic patterning genes identifies conserved genetic interactions

Phenotypic robustness is evidenced when single-gene mutations do not result in an obvious phenotype. It has been suggested that such phenotypic stability results from 'buffering' activities of homologous genes as well as non-homologous genes acting in parallel pathways. One approach to characterizing mechanisms of phenotypic robustness is to identify genetic interactions, specifically, double mutants where buffering is compromised. To identify interactions among genes implicated in posterior patterning of the Caenorhabditis elegans embryo, we measured synthetic lethality following RNA interference of 22 genes in 15 mutant strains. A pair of homologous T-box transcription factors (tbx-8 and tbx-9) is found to interact in both C. elegans and C. briggsae, indicating that their compensatory function is conserved. Furthermore, a muscle module is defined by transitive interactions between the MyoD homolog hlh-1, another basic helix-loop-helix transcription factor, hnd-1, and the MADS-box transcription factor unc-120. Genetic interactions within a homologous set of genes involved in vertebrate myogenesis indicate broad conservation of the muscle module and suggest that other genetic modules identified in C. elegans will be conserved

Universal λ-[lambda]-tracking for nonlinearly-perturbed systems in the presence of noise

For a class l of multivariable, nonlinearly-perturbed, linear, minimum-phase systems of relative degree one, with output measurement noise of Sobolev class W1,00 (absolutely continuous on compact intervals, and bounded with essentially bounded derivative), the following servomechanism problem is solved..

On tracking and disturbance rejection by adaptive control

For linear minimum-phase relative-degree-one systems subject to disturbances and nonlinear perturbations, results pertaining to disturbance rejection and adaptive tracking of constant reference signals are presented and discussed in the context of related results in the literature